Simplify the following expression: $ q = \dfrac{-9}{8} - \dfrac{3a}{-a - 2} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-a - 2}{-a - 2}$ $ \dfrac{-9}{8} \times \dfrac{-a - 2}{-a - 2} = \dfrac{9a + 18}{-8a - 16} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{3a}{-a - 2} \times \dfrac{8}{8} = \dfrac{24a}{-8a - 16} $ Therefore $ q = \dfrac{9a + 18}{-8a - 16} - \dfrac{24a}{-8a - 16} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{9a + 18 - 24a }{-8a - 16} $ Distribute the negative sign: $q = \dfrac{9a + 18 - 24a}{-8a - 16}$ $q = \dfrac{-15a + 18}{-8a - 16}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{15a - 18}{8a + 16}$